What S My Rule

What’s My Rule?

1st 2nd 3rd 4th 5th 6th 7th

1.  Find a pattern in the sequence of figures and use your tiles to construct and sketch the next three figures.

2.  Use your tiles to build the 10th figure for this sequence. Draw a sketch of the figure.

3.  a. Complete the table. Describe the pattern in the sequence.

Step / 1st / 2nd / 3rd / 4th / 5th / 6th / … / 10th / 20th
Number
of Tiles

b. Describe precisely how you would build the 20th figure.

c. How many tiles would be needed?

4.  Describe what the 50th figure would look like and how many tiles it would contain.

5.  Write a formula (rule) for determining the number of tiles for any figure number n.

6.  Explain why your formula works.

Growing Tile Pattern

1.  Use your models and any patterns you notice to complete the table.

Figure
# / # of Tiles
Input / Output
n /

2.  Name the rule in a word sentence:

3.  Name the rule using variables:

4.  Construct a graph of the first 5 terms of

the pattern.

Graphing on the TI-73 Explorer

Compare the graphs of the figure number and number of tiles

with the graph of the rule (function).

Graphing a Scatter Plot

1. Press LIST.

2. Enter the figure numbers in L1.

3. Enter the corresponding number of tiles in L2.

4. Press 2nd.

5. Press PLOT. (This is the y= button).

6. Select 1. ENTER.

7. Select ON. ENTER.

8. Arrow down to "Type." Select the scatter plot. ENTER.

9. Check that Xlist = L1 and Ylist = L2.

10. Press WINDOW. Enter the appropriate minimums, maximums, and scale.

(Optional: ZOOM, ZOOMStat will automatically adjust the window to fit the data.)

11. Press GRAPH.

Graphing Equations

1.  Press y=.

2.  Enter the rule that you created.

3.  Press GRAPH.

4.  Compare the graphs.

(Optional: ZOOM, ZStandard to view the full rectangular coordinate grid.

Growing Geometric Patterns

1st 2nd 3rd 4th 5th 6th

1.  Find a pattern in the sequence of figures and use your tiles to construct and sketch the next three figures.

2.  Use your tiles to build the 10th figure for this sequence. Draw a sketch of the figure.

3.  a. Describe the pattern in the sequence.

b. Describe precisely how you would build the 20th figure.

c. How many tiles would the figure contain?

4.  Complete the table.

Figure / 1st / 2nd / 3rd / 4th / 5th / 6th / … / 10th / 20th / nth
Number
of Tiles

5.  Write a formula (rule) for determining the number of tiles for any figure number n.

6.  Explain why your formula works.

BColeman 11_2014